What are the specific requirements of the Turing test?
The "Turing Test" is generally taken to mean an updated version of the Imitation Game Alan Turing proposed in his 1951 paper of the same name. An early version had a human (male or female) and a computer, and a judge had to decide which is which, and what gender they were if human. If they were correct less than 50% then the computer was considered "intelligent."

The current generally accepted version requires only one contestant, and a judge to decide whether it is human or machine. So yes, sometimes this will be a placebo, effectively, if we consider a human to be a placebo.

Your first and fourth questions are related - and there are no strict guidelines. If the computer can fool a greater number of judges then it will of course be considered a better AI.

The University of Toronto has a validity section in this paper on Turing, which includes a link to Jason Hutchens' commentary on why the Turing test may not be relevant (humans may also fail it) and the Loebner Prize, a formal instantiation of a Turing Test .